华东师范大学学报（自然科学版） >

2015 , Vol. 2015 >Issue 1: 75 - 83

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.01.009

应用数学与基础数学

关于一类高阶微分方程的复振荡结果

  • 胡梦薇 ,
  • 黄志刚 ,
  • 孙桂荣
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  • 1. 苏州科技学院 数理学院, 江苏 苏州 215009; 2. 许昌电气职业学院, 河南 许昌 461000

收稿日期: 2013-12-01

  网络出版日期: 2015-03-29

基金资助

国家自然科学基金(11001057);

江苏省自然科学基金(BK2010234);

江苏省青蓝工程, 苏州科技学院研究生科研创新工程项目(SKCX12S_043

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An oscillation result for some higher order linear differential equations

  • HU Meng-Wei ,
  • HUANG Zhi-Gang ,
  • SUN Gui-Rong
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  • 1. Department of Mathematics, University of Science and Technology of Suzhou, Suzhou Jiangsu 215009, China
    2. Xuchang Eelectrical Vocational College, Xuchang Henan 461000, China

Received date: 2013-12-01

  Online published: 2015-03-29

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摘要

运用微分方程复振荡理论,研究了系数是整函数的高阶微分方程解的零点分布问题,在对方程的某个系数做小的扰动的情况下,得到了方程的超越解的零点收敛指数都为无穷.

关键词： 复微分方程; 整函数; 增长级; 零点收敛指数

本文引用格式

胡梦薇 , 黄志刚 , 孙桂荣 . 关于一类高阶微分方程的复振荡结果[J]. 华东师范大学学报（自然科学版）, 2015 , 2015(1) : 75 -83 . DOI: 10.3969/j.issn.1000-5641.2015.01.009

Abstract

The distribution of zeros of solutions of higher order linear differential equations with entire coefficients was investigated by using complex oscillation theory of linear differential equations. It was proved that the exponent of convergence of zeros of every transcendental solution of the equations is infinite if given a small perturbation to one of the coefficients.

Key words： complex differential equations; entire function; growth of order; exponent of convergence of zeros

参考文献

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